This is a concept of ATC, which refers to aircraft which are not adequately separated from each other. Were two aircraft to be in this situation, each would be given 'essential traffic information' on the other by ATC. 'Traffic information' is the position, altitude and heading (direction) of the aircraft, though any other information the controller thinks is relevant (the aircraft type, for instance) can be added too.
The UK Civil Aviation Authority, in its Manual of Air Traffic Services, has this to say about 'essential traffic':
Essential traffic is traffic which is separated for any period by less than the specified standard separation. It is normally passed in situations when ATS surveillance systems are not available.
Indeed, this is the only circumstance under which I've encountered it. My job as an air traffic simulator pilot ('blip driver', to use our slang) for trainee controllers currently concerns contrived situations in which the trainee's radar has failed. Radar is nitrogen to air traffic control's air. ATC is relatively little without it. Depending on your perspective its absence greatly simplifies or greatly complicates the job, making it a pain in the ass and/or more boring than the channel tunnel drilling machine.
Sorry.
Most would agree, however, that when radar fails ATC goes back to the stone age. We are plunged instantly into the sickly treacle of 'procedural' controlling, bound by the 'Separation Standards' section of the Manual of Air Traffic Services. I could easily fill screens on these procedures, but I'll go easy on your eyes (and my aggregate downvotes) for now.
Procedural controlling, rather than radar control, is done using navigation aids (VORs, DMEs and similar equipment for measuring bearings and distances), position reports, level reports and pilot estimates. Although extremely convoluted and low-capacity compared to radar control, it is the only option in places where there is no radar coverage, such as the ocean. It is very safe though, and is often the first measure against which to check a proposed plan for aircraft under radar control: is the plan procedurally safe?. Radar control is often done in a way that either ensures, or makes it easy to establish, procedural separation if the radar fails.
To my knowledge, there has never been a serious failure of civil ATC radar (i.e. one not recovered by redundancy) in the UK.
Procedural separation is what flight progress strips are used to plan. Procedural sectors of airspace (like the ocean) just have a flight progress strip board and a telephone at the controller position. The strips are arranged vertically, either in ascending order of aircraft altitude, or in order of estimated aircraft times over particular points. The altitudes and/or times on the strips (there is one for each aircraft) are used to determine whether any aircraft are 'in the way' of others wanting to climb or descend. If aircraft are just passing each other in the air at separated levels this isn't needed, but as inevitably happens, there's always a few (dozen) that spoil it for everyone and want to climb or descend through the levels of others.
In this case you have to establish some kind of lateral separation, which is what radar is so useful for, and what makes its absence such a bind. The only way to do it is using established navigation points (called Exact Reporting Points, which must be legally certified as being so). You could get a pair of aircraft to fly diverging bearings from a certain navigation beacon, use their estimated times overhead a certain point, or their distances from a certain point to establish lateral separation. This allows you to safely lose vertical separation so those awkward aircraft can get their climbs or descents.
Fine fine fine, but what of essential traffic information? Well, there is often a flurry of this following a radar failure. When the radar is operating, the lateral separation the controller is using (i.e. being able to see on radar from the distances, directions and perhaps speeds of the aircraft involved, that they are not going to hit each other) is often invalid under procedural rules. This means that once the radar fails and the procedural darkness descends, pretty much any aircraft within the controller's sector that aren't separated vertically (usually by 1,000ft), regardless of how many miles they are apart, are not technically separated.
*gulp*
So, amongst the first things you'll hear on the communications frequency, at least after this:
"All stations, all stations, radar has failed, I say again the radar has failed; all aircraft return to previously-assigned headings and levels."
...and once the controller has established the levels of all their aircraft, is the words "essential traffic information."
Two aircraft thirty miles apart travelling in opposite directions, altitude-separated by less than 1,000ft are 'essential traffic' to each other if no procedural separation (and that means the aforementioned time, distance or track-based separation) is established, and chances are it isn't. The controller then has to give both aircraft traffic information on the other, now-'conflicting' aircraft. They probably feel quite stupid giving some of it. Bold type is the controller.
"Delta 459, report your level?"
"Passing flight level 80, Delta 459."
"Lufthansa 768, report your level?"
"Passing flight level 75, Lufthansa 768."
"Lufthansa 768, roger; essential traffic information: a Boeing 747 departing from Nodehaven, last known position fifteen miles North of NODE, tracking North, flight level 80 and climbing."
"Traffic copied, Lufthansa 768."
"Delta 459, essential traffic information: an Airbus A340 departing Nodehaven to the South, last known position fifteen miles South of NODE, tracking South, flight level 75 and climbing."
"Traffic copied, Delta 459."
This is a deliberately-absurd example to get the point across, although if two aircraft were in that situation then they would be given traffic information on each other in that manner. One of them - most likely the lower of the two - would also be stopped from climbing to quickly establish vertical separation between the two.
The most common phrase used by ATC during a radar failure situation is "report your level," for obvious reasons. In fact, such requests for information from aircraft usually precede the passing of essential traffic information, as it may not be immediately obvious to the controller which aircraft are not currently separated procedurally.